Trivial points in the maximal ideal space of \(H^\infty\) (Q2705835)

Let \(M(H^\infty)\), \(M(L^\infty)\) denote the maximal ideal space of \(H^\infty\), \(L^\infty\), \(s(x,y)\) denote the pseudo-hyperbolic distance between \(x\), \(y\) in \(M(H^\infty)\). Let \(P(x)= \{y\in M(H^\infty): s(x,y)< 1\}\). If \(P(x)= \{x\}\), \(x\) is called trivial. Let \(S\), \(G\) be the sets of trivial and nontrivial points of \(M(H^\infty)\). The author proved that there exists \(x_0\in S\setminus M(L^\infty)\) such that \(x_0\notin\overline{P(x)}\) for every \(x\in G\setminus \mathbb{D}\).